Question

Imagine a number of isoquants drawn for a particular Cobb-Douglas production function. If technology *decreased*, what would happen to those isoquants?

Answer 1

The Cobb-Douglas production function is represented as below -

F(X₁, X₂) = (X₁)1/2 * (X₂)^1/2

So, this is a rectangular hyperbola function and hence isoquants are rectangular hyperbola and converging towards origin.

Therefore, Marginal rate of technical substitution can be calculated as below -

F(X₁, X₂) = (X₁)^1/2 * (X₂)^1/2

The Y isoquant of the Cobb-Douglas function is defined as -

Y² = X₁* X₂

=> X₂ = Y² / X₁

On differentiating, we will get -

dX₂/dX₁ = Y²/X₁² = X₂/X₁.

Therefore, MRTS (X₁, X₂) = X₂/X₁

Thus, the MRTS is diminishing which leads to decreased and converged isoquants.